italian version

Aims :

To impart the basic elements of the differential equations of Mathematical Physics and of their solution methods: transport equations, the heat equation, the diffusion equation, the Poisson and Laplace equations.

Topics :

1. Brief introduction to functional spaces.
2. General introduction to partial differential equations.
3. First-order equations: general concepts, quasi-linear equations and the Cauchy problem, characteristics.
4. Second order equations: general concepts and classification; canonical form and characteristics.
5. Relevant equations: the wave equation, the heat equation, the diffusion equation, the Laplace and the Poisson equations. Main properties and theorems.
6. Important examples and solutions methods for first-order and for second order elliptic, parabolic and hyperbolic equations. Eigenfunctions expansion, Fourier transforms, integration along the characteristics and similarity techniques.
7. Finite difference numerical methods for partial differential equations.

Textbooks :

Lecture notes from the teacher.

Exam :

Oral only.

Tutorial Session :

Wednesday 10.00 a.m. - 3.00 p.m. and by appointment.